Consider the FM signal: s(t) = 8cos[2πx105t+3∫-∞t m(t)dt]
Consider the FM signal: s(t) = 8cos[2πx105t+3∫-∞t m(t)dt]
(a) Determine the instantaneous frequency and instantaneous phase of s(t).
(b) Determine the frequency deviation and phase deviation of s(t)
(c) Suppose the maximum value of |m(t)| is 4000 π, determine the maximum frequency deviation of s(t)
(d) If m(t) has a bandwidth of 5 kHz, determine the bandwidth of s(t)
Homework Answers
Consider an FM system where the modulated signal is
Consider an FM system where the modulated signal is s(t) = 10 cos (2πfct + 2πkf∫0t m(τ)dτ)where the carrier frequency is fc = 100 MHz. The modulation signal is m(t) = 10 cos(2πfmt), where fm = 3 kHz. (a) Assuming that kf = 10, what is the approximate bandwidth of s(t)? (b) Find the instantaneous frequency fi(t) of s(t). What are the maximum and minimum values of fi(t) ?
5. Consider the following message signal: m(t) -2 .3 10 Assume that the carrier frequency is f ar...
5. Consider the following message signal: m(t) -2 .3 10 Assume that the carrier frequency is f are kf = 105, kp-25 respectively. 108 Hz, and frequency and phase deviation constants Find the maximum and minimum frequency deviation for FM, and sketch the FM wave for a duration of 103 seconds shown in the above figure (5 points). a. b. Find the maximum and minimum frequency deviation for PM, sketch the PM wave for a duration of 103 seconds shown...
Consider a FM system that is used to communicate the following message signal: S. m(t) 20...
Consider a FM system that is used to communicate the following message signal: S. m(t) 20 0.05 0.1 015 10 -0.05 with a frequency deviation constant ky 10, and a message bandwidth of W =15 kHz the one-sided noise power-spectral density in the transmission channel is No= 10-8 W/Hz, and an attenuation of 10 is introduced during transmission in the channel as well. a. What is the average-to-peak-power ratio of the message (or, equivalently the power content of the normalized...
Consider a FM system that is used to communicate the following message signal: S. m(t) 20...
Consider a FM system that is used to communicate the following message signal: S. m(t) 20 0.05 0.1 015 10 -0.05 with a frequency deviation constant ky 10, and a message bandwidth of W =15 kHz the one-sided noise power-spectral density in the transmission channel is No= 10-8 W/Hz, and an attenuation of 10 is introduced during transmission in the channel as well. a. What is the average-to-peak-power ratio of the message (or, equivalently the power content of the normalized...
Q2 The output signal of an angle modulator is given as V(t) = 6 cos(2000000net +...
Q2 The output signal of an angle modulator is given as V(t) = 6 cos(2000000net + 40 cos(2000xt) + 15cos (400nt)) (v) Determine the following: The average power of the signal. b) The carrier frequency of the signal. The instantaneous frequency of the signal. d) The instantaneous maximum frequency deviation of the signal. e) The wavefom of the message signal, assuming a frequency modulation (FM). f) The modulation index, assuming a FM. Is it a broadband FM or narrowband FM...
5. Consider the following message signal: -2 Assume that the carrier frequency is f are kr 105, k...
5. Consider the following message signal: -2 Assume that the carrier frequency is f are kr 105, kp 25 respectively. 108 Hz, and frequency and phase deviation constants Find the maximum and minimum frequency deviation for FM, and sketch the FM wave for a duration of 103 seconds shown in the above figure (5 points). a. b. Find the maximum and minimum frequency deviation for PM, sketch the PM wave for a duration of 103 seconds shown in the above...
b) The figure below shows an FM demodulator. s'(t)Envelope detector Demodulated signal s(t) Differentiator Figure 4: Question 2(b) In the system above, the differentiator performs the time-differ...
b) The figure below shows an FM demodulator. s'(t)Envelope detector Demodulated signal s(t) Differentiator Figure 4: Question 2(b) In the system above, the differentiator performs the time-differentiation operation s'(t) = as(t). Also, the envelope detector is assumed to be ideal, capable of extracting the envelope of the incoming signal perfectly. Describe, by equations, how the above FM demodulator may exactly recover the message signal from the FM signal. (6%) (c) Is the FM demodulator in Question 2(b) a coherent detector,...
Find the instantaneous frequency of the next signal at t = 4. (a) x(t) = 10...
Find the instantaneous frequency of the next signal at t = 4. (a) x(t) = 10 cos[20xt+10 sin(t/4)) (b) x(t) = 262719) () X(t)=10[cos(2nt) cos(atº/4) + sin(24t) sin( nt/ 4)] Suppose that the information signal is as shown in the following figure. When each modulating this signal using 100KHz as the carrier frequency, find the frequency shift and phase shift when FM is modulated with 5,=10. What is the maximum frequency shift and maximum phase shift? 0.5+ -0.5 ost Suppose...
Drill Problem 4.3 with extension 2. A signal is transmitted by an FM transmitter with a...
Drill Problem 4.3 with extension 2. A signal is transmitted by an FM transmitter with a frequency deviation constant Ja of 5 Hz per unit of message signal m(t) where m(t) = cos(40rt)+2sin(60) Assuming a zero initial phase, i.e., P()-, for this transmitted signal, (a) determine the expression of the phase deviation P(in radian and the peak phase deviation; 1 do(t) (b) determine the expression of the frequency deviation 2t hertz and the peak frequency deviation. dt in Solution
Drill...
Question 4: (20 points) An FM signal is modulated with message m(t)Am cos(2Tmt). The measured amp...
Question 4: (20 points) An FM signal is modulated with message m(t)Am cos(2Tmt). The measured amplitude spectrum, SPM(f), is shown below: Amplitude spectrum of the frequency modulated signal 2 -2 5000 4000 3000 2000 -1000 1000 2000 3000 4000 5000 frequency f [Hz] a) What is the carrier frequency fe? b) What is the message frequency fm c) What is the FM modulation index Bf? Is it a narrowband or a wideband signal? d) Using Carson's rule, estimate the transmission...
5. Consider the following message signal: m(t) -2 .3 10 Assume that the carrier frequency is f are kf = 105, kp-25 respectively. 108 Hz, and frequency and phase deviation constants Find the maximum and minimum frequency deviation for FM, and sketch the FM wave for a duration of 103 seconds shown in the above figure (5 points). a. b. Find the maximum and minimum frequency deviation for PM, sketch the PM wave for a duration of 103 seconds shown...
Consider a FM system that is used to communicate the following message signal: S. m(t) 20 0.05 0.1 015 10 -0.05 with a frequency deviation constant ky 10, and a message bandwidth of W =15 kHz the one-sided noise power-spectral density in the transmission channel is No= 10-8 W/Hz, and an attenuation of 10 is introduced during transmission in the channel as well. a. What is the average-to-peak-power ratio of the message (or, equivalently the power content of the normalized...
Consider a FM system that is used to communicate the following message signal: S. m(t) 20 0.05 0.1 015 10 -0.05 with a frequency deviation constant ky 10, and a message bandwidth of W =15 kHz the one-sided noise power-spectral density in the transmission channel is No= 10-8 W/Hz, and an attenuation of 10 is introduced during transmission in the channel as well. a. What is the average-to-peak-power ratio of the message (or, equivalently the power content of the normalized...
Q2 The output signal of an angle modulator is given as V(t) = 6 cos(2000000net + 40 cos(2000xt) + 15cos (400nt)) (v) Determine the following: The average power of the signal. b) The carrier frequency of the signal. The instantaneous frequency of the signal. d) The instantaneous maximum frequency deviation of the signal. e) The wavefom of the message signal, assuming a frequency modulation (FM). f) The modulation index, assuming a FM. Is it a broadband FM or narrowband FM...
5. Consider the following message signal: -2 Assume that the carrier frequency is f are kr 105, kp 25 respectively. 108 Hz, and frequency and phase deviation constants Find the maximum and minimum frequency deviation for FM, and sketch the FM wave for a duration of 103 seconds shown in the above figure (5 points). a. b. Find the maximum and minimum frequency deviation for PM, sketch the PM wave for a duration of 103 seconds shown in the above...
b) The figure below shows an FM demodulator. s'(t)Envelope detector Demodulated signal s(t) Differentiator Figure 4: Question 2(b) In the system above, the differentiator performs the time-differentiation operation s'(t) = as(t). Also, the envelope detector is assumed to be ideal, capable of extracting the envelope of the incoming signal perfectly. Describe, by equations, how the above FM demodulator may exactly recover the message signal from the FM signal. (6%) (c) Is the FM demodulator in Question 2(b) a coherent detector,...
Find the instantaneous frequency of the next signal at t = 4. (a) x(t) = 10 cos[20xt+10 sin(t/4)) (b) x(t) = 262719) () X(t)=10[cos(2nt) cos(atº/4) + sin(24t) sin( nt/ 4)] Suppose that the information signal is as shown in the following figure. When each modulating this signal using 100KHz as the carrier frequency, find the frequency shift and phase shift when FM is modulated with 5,=10. What is the maximum frequency shift and maximum phase shift? 0.5+ -0.5 ost Suppose...
Drill Problem 4.3 with extension 2. A signal is transmitted by an FM transmitter with a frequency deviation constant Ja of 5 Hz per unit of message signal m(t) where m(t) = cos(40rt)+2sin(60) Assuming a zero initial phase, i.e., P()-, for this transmitted signal, (a) determine the expression of the phase deviation P(in radian and the peak phase deviation; 1 do(t) (b) determine the expression of the frequency deviation 2t hertz and the peak frequency deviation. dt in Solution
Drill...
Question 4: (20 points) An FM signal is modulated with message m(t)Am cos(2Tmt). The measured amplitude spectrum, SPM(f), is shown below: Amplitude spectrum of the frequency modulated signal 2 -2 5000 4000 3000 2000 -1000 1000 2000 3000 4000 5000 frequency f [Hz] a) What is the carrier frequency fe? b) What is the message frequency fm c) What is the FM modulation index Bf? Is it a narrowband or a wideband signal? d) Using Carson's rule, estimate the transmission...
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